Solved Exercises on Area with Unit Squares in Grade 3

Master area with unit squares: counting squares, calculating area, comparing areas, and problem solving through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting unit squares
Exercise 1
Find the area of the rectangle below by counting unit squares:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Rectangle: 4 rows × 5 columns
Definition:

Unit square: A square with sides of length 1 unit. Area = 1 square unit

Area: The amount of space inside a shape measured in square units

Counting method:
  1. Count each unit square inside the shape
  2. Make sure to count systematically (row by row or column by column)
  3. Add up all the unit squares to get the total area
Shape
Rectangle
Unit Squares
20 squares
Area
20 sq units
Step 1: Count squares in each row

Row 1: 5 squares, Row 2: 5 squares, Row 3: 5 squares, Row 4: 5 squares

Step 2: Add all squares together

5 + 5 + 5 + 5 = 20 squares

Step 3: Express the area

Area = 20 square units

Area = 20 square units
Final answer:

The area of the rectangle is 20 square units

Applied rules:

• Counting: Every unit square contributes 1 square unit to the area

• Systematic approach: Count row by row to avoid missing squares

• Units: Always express area in square units

2 Area of irregular shape
Exercise 2
Find the area of the irregular shape by counting unit squares:
Irregular shape made of unit squares
Definition:

Irregular shape: A shape that does not have equal sides or angles

Unit square method: Works for ANY shape by counting filled squares

Shape
Irregular
Unit Squares
22 squares
Area
22 sq units
Step 1: Count systematically by rows

Row 1: 4 squares, Row 2: 4 squares, Row 3: 5 squares, Row 4: 6 squares, Row 5: 4 squares, Row 6: 4 squares

Step 2: Add all squares together

4 + 4 + 5 + 6 + 4 + 4 = 27 squares

Step 3: Count accurately

Actually counting: 4+4+5+6+4+4 = 27 squares

Step 4: Express the area

Area = 27 square units

Area = 27 square units
Final answer:

The area of the irregular shape is 27 square units

Applied rules:

• Counting: Works for regular and irregular shapes

• Systematic approach: Count row by row or column by column

• Accuracy: Double-check your counting

3 Using multiplication for rectangles
Exercise 3
Find the area of the rectangle using multiplication:
Length = 6 units, Width = 4 units
Rectangle: 6 units long × 4 units wide
Definition:

Rectangle area formula: Area = Length × Width

Multiplication shortcut: Instead of counting, multiply dimensions

Length
6 units
Width
4 units
Area
24 sq units
Step 1: Identify dimensions

Length = 6 units, Width = 4 units

Step 2: Apply the formula

Area = Length × Width = 6 × 4

Step 3: Calculate the product

6 × 4 = 24

Step 4: Express the area

Area = 24 square units

Area = 6 × 4 = 24 square units
Final answer:

The area of the rectangle is 24 square units

Applied rules:

• Multiplication rule: Area of rectangle = length × width

• Efficiency: Multiplication is faster than counting squares

• Verification: You can still count squares to check

Rules and methods, laws,...
Area = Length × Width
Rectangle Area Formula
Rule 1
Area = Count of unit squares
Basic counting method
Rule 2
Area = Length × Width
Rectangle formula
Rule 3
Area in square units
Always use square units
Key definitions:

Area: The amount of space inside a 2D shape

Unit square: A square with sides of 1 unit length

Square unit: The unit used to measure area

Complete methodology:
  1. Identify the shape: Rectangle, square, or irregular
  2. Choose the method: Counting squares or multiplication
  3. Apply the method: Count systematically or multiply dimensions
  4. Express the answer: In square units
Tip 1: For rectangles, always multiply length by width.
Tip 2: Count row by row to avoid missing squares.
Tip 3: Always write "square units" after your answer.
Tip 4: You can use both methods to check your work.
Common errors: Forgetting square units, miscounting, mixing up length and width.
Key concepts: Area measures space inside shapes, unit squares fill the space.
Formulas to know by heart:

• Rectangle area: Area = Length × Width

• Square area: Area = Side × Side = Side²

• Any shape: Area = Total number of unit squares

• Units: Always express area in square units

Solution: Exercises 4 to 5
4 Comparing areas
Exercise 4
Which rectangle has a larger area?
Rectangle A: 5 units long × 3 units wide
Rectangle B: 4 units long × 4 units wide
Rectangle A (5×3)
Rectangle B (4×4)
Definition:

Comparing areas: Calculate each area and compare the results

Rectangle A
5×3=15
Rectangle B
4×4=16
Comparison
B > A
Step 1: Calculate Rectangle A's area

Area of A = Length × Width = 5 × 3 = 15 square units

Step 2: Calculate Rectangle B's area

Area of B = Length × Width = 4 × 4 = 16 square units

Step 3: Compare the areas

16 > 15, so Rectangle B has the larger area

Rectangle B has the larger area (16 vs 15 square units)
Final answer:

Rectangle B has a larger area (16 square units) than Rectangle A (15 square units)

Applied rules:

• Comparison: Calculate each area separately

• Multiplication: Use the area formula for rectangles

• Analysis: Compare numerical results

5 Word problem with area
Exercise 5
Sarah wants to plant flowers in her rectangular garden. The garden is 8 feet long and 5 feet wide. If each flower needs 1 square foot of space, how many flowers can she plant?
Definition:

Word problems: Apply area concepts to real-life situations

Garden size
8×5=40
Space per flower
1 sq ft
Number of flowers
40 flowers
Step 1: Identify the dimensions

Garden length = 8 feet, Garden width = 5 feet

Step 2: Calculate the area of the garden

Area = Length × Width = 8 × 5 = 40 square feet

Step 3: Determine how many flowers fit

If each flower needs 1 square foot, then 40 square feet can hold 40 flowers

Step 4: State the final answer

Sarah can plant 40 flowers in her garden

Sarah can plant 40 flowers in her garden
Final answer:

Sarah can plant 40 flowers in her garden

Applied rules:

• Real-world application: Area helps determine capacity

• Unit conversion: Square feet correspond to number of items

• Problem solving: Connect math to practical situations

Area Fundamentals and Key Concepts
Area = Length × Width
Rectangle Area Formula
Key definitions:

Area: The amount of space inside a 2D shape measured in square units

Unit square: A square with sides of length 1 unit

Square unit: The standard unit for measuring area

Rectangle: A 4-sided shape with 4 right angles

Dimension: Length and width measurements of a shape

Complete methodology:
  1. Identify the shape: Recognize if it's a rectangle, square, or irregular shape
  2. Choose the method: Counting squares for any shape, or multiplication for rectangles
  3. Apply the method: Count systematically or multiply length by width
  4. Verify the result: Double-check by using an alternative method
  5. Express in proper units: Always state the answer in square units
Tip 1: For rectangles, always multiply length by width to find area quickly.
Tip 2: Count row by row or column by column to avoid missing squares.
Tip 3: Remember that area is always expressed in square units.
Tip 4: You can use both counting and multiplication to verify your answer.
Tip 5: Draw the shape on grid paper to visualize the unit squares.
Common errors: Forgetting to use square units, miscounting squares, confusing area with perimeter.
Key concepts: Area measures the inside space, unit squares fill that space completely.
Patterns: Rectangles with the same perimeter can have different areas.
Applications: Flooring, painting walls, gardening, construction projects.
Formulas to know by heart:

• Rectangle area: Area = Length × Width

• Square area: Area = Side × Side = Side²

• Any shape: Area = Total number of unit squares inside

• Units: Always express area in square units (sq units, ft², m², etc.)

• Verification: Counting squares should match multiplication result

Examples of area in daily life: Carpet for a room, paint for a wall, tiles for a floor, garden plots for vegetables.
Visual strategies: Color-code rows when counting, use multiplication tables for quick calculations.

Questions & Answers

Question: Why do we need to count unit squares to find area? Can't we just measure the sides?

Answer: Great question Johnny! Counting unit squares is important because:

  • It helps you UNDERSTAND what area really means - the space inside a shape
  • It works for ANY shape, even irregular ones that don't have simple formulas
  • It builds the foundation for the multiplication method you'll learn

When you count unit squares, you're literally seeing how much space is inside. Later, you'll learn that for rectangles, you can multiply length × width instead of counting every single square. But counting first helps you understand WHY multiplication works!

Think of it like learning addition before multiplication - counting squares is like addition, and multiplying dimensions is like multiplication!

Question: What's the difference between area and perimeter? They both measure shapes, right?

Answer: Excellent question Sophie! Area and perimeter measure different things:

  • Area: Measures the SPACE INSIDE a shape (like how much carpet covers a floor)
  • Perimeter: Measures the DISTANCE AROUND a shape (like how much fence goes around a yard)

Think of a rectangle like a picture frame:

  • The area is the space where the picture goes (inside the frame)
  • The perimeter is the wooden frame itself (around the edges)

Area is measured in square units (like square feet), while perimeter is measured in regular units (like feet). Two shapes can have the same perimeter but different areas!

Question: How do I know when to use counting versus multiplication to find area?

Answer: Here's a helpful guide for choosing the right method:

  1. Use counting when:
    • The shape is irregular (not a perfect rectangle)
    • You want to understand what area means
    • The shape is small and easy to count
    • You want to verify your multiplication answer
  2. Use multiplication when:
    • The shape is a rectangle or square
    • You know the length and width measurements
    • The shape is large (counting would take too long)
    • You want a quick answer

For rectangles: Area = Length × Width is always faster than counting. But counting helps you understand why this formula works! It's like having two tools - use the one that's most efficient for the job.